Go up the Big Buddha
The Big Buddha is definitely the highlight of visiting Phuket. The statue is 45 m high and it is located on top of one of the highest viewpoints in the area where you will be able to get a panoramic view of the entire southern coastal area of Phuket. The ride up there is quite steep but incredible and you should be able to go up there with a rented moped just fine. There are some really steep sections but the road is good and as long as you take it slow when coming down, you should have no trouble getting up and down the Big Buddha safely.
Once you are at the top, you can park your moped at a designated parking area and you will have to walk up a bit to the viewing platform and a bit more to the Big Buddha statue itself. From the platform, you can see the entire southern coast of Phuket with Promthep Cape, Nai Harn, and Rawai beaches all in your vicinity. You can even see Kata beach from behind if you walk a little further to the other side of the platform.